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//===-- Half-precision cos(x) function ------------------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "src/math/cosf16.h"
#include "hdr/errno_macros.h"
#include "hdr/fenv_macros.h"
#include "sincosf16_utils.h"
#include "src/__support/FPUtil/FEnvImpl.h"
#include "src/__support/FPUtil/FPBits.h"
#include "src/__support/FPUtil/cast.h"
#include "src/__support/FPUtil/except_value_utils.h"
#include "src/__support/FPUtil/multiply_add.h"
#include "src/__support/macros/optimization.h"
namespace LIBC_NAMESPACE_DECL {
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
constexpr size_t N_EXCEPTS = 4;
constexpr fputil::ExceptValues<float16, N_EXCEPTS> COSF16_EXCEPTS{{
// (input, RZ output, RU offset, RD offset, RN offset)
{0x2b7c, 0x3bfc, 1, 0, 1},
{0x4ac1, 0x38b5, 1, 0, 0},
{0x5c49, 0xb8c6, 0, 1, 0},
{0x7acc, 0xa474, 0, 1, 0},
}};
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
LLVM_LIBC_FUNCTION(float16, cosf16, (float16 x)) {
using FPBits = fputil::FPBits<float16>;
FPBits xbits(x);
uint16_t x_u = xbits.uintval();
uint16_t x_abs = x_u & 0x7fff;
float xf = x;
// Range reduction:
// For |x| > pi/32, we perform range reduction as follows:
// Find k and y such that:
// x = (k + y) * pi/32
// k is an integer, |y| < 0.5
//
// This is done by performing:
// k = round(x * 32/pi)
// y = x * 32/pi - k
//
// Once k and y are computed, we then deduce the answer by the cosine of sum
// formula:
// cos(x) = cos((k + y) * pi/32)
// = cos(k * pi/32) * cos(y * pi/32) -
// sin(k * pi/32) * sin(y * pi/32)
#ifndef LIBC_MATH_HAS_SKIP_ACCURATE_PASS
// Handle exceptional values
if (auto r = COSF16_EXCEPTS.lookup(x_abs); LIBC_UNLIKELY(r.has_value()))
return r.value();
#endif // !LIBC_MATH_HAS_SKIP_ACCURATE_PASS
// cos(+/-0) = 1
if (LIBC_UNLIKELY(x_abs == 0U))
return fputil::cast<float16>(1.0f);
// cos(+/-inf) = NaN, and cos(NaN) = NaN
if (xbits.is_inf_or_nan()) {
if (xbits.is_signaling_nan()) {
fputil::raise_except_if_required(FE_INVALID);
return FPBits::quiet_nan().get_val();
}
if (xbits.is_inf()) {
fputil::set_errno_if_required(EDOM);
fputil::raise_except_if_required(FE_INVALID);
}
return x + FPBits::quiet_nan().get_val();
}
float sin_k, cos_k, sin_y, cosm1_y;
sincosf16_eval(xf, sin_k, cos_k, sin_y, cosm1_y);
// Since, cosm1_y = cos_y - 1, therefore:
// cos(x) = cos_k * cos_y - sin_k * sin_y
// = cos_k * (cos_y - 1 + 1) - sin_k * sin_y
// = cos_k * cosm1_y - sin_k * sin_y + cos_k
return fputil::cast<float16>(fputil::multiply_add(
cos_k, cosm1_y, fputil::multiply_add(-sin_k, sin_y, cos_k)));
}
} // namespace LIBC_NAMESPACE_DECL
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